in left top corner you will find search. It works just fine but I want to have items showed in template "mcol.php". But if I open one page where template is "thumb.php" I get also search results in same template. Can I change it, so that I always get search results in "mcol" template?
The menu configration has two options to assign a layout, for the first page and for the other pages. The search result uses the 'first page' layout.
Probably makes more sence to change this to 'use other pages' will consider that.
In the original default_mcol.php you will see how the template changes if a single product is shown, that is when the 't' parameter is set.